In the code-division multiple access (CDMA) downlink (base station to mobile station communication link), equalization can restore the orthogonality lost in multipath channels, and exceed the performance attained by a Rake receiver. For practical implementation of the equalizers, two forms of an adaptive least-mean-square (LMS) algorithm have been proposed. Both forms operate on the individual received chips, however, the straightforward LMS algorithm updates the weights at every chip time, whereas the second approach (called “LMS-G”) performs an extra correlation at the equalizer output and updates the weights at the symbol rate. It has also been shown that with careful adjustment of the LMS step size, μ, the LMS-G algorithm is superior for both SISO (single input single output) and MIMO (multiple input multiple output) equalizers.
Unfortunately, the adaptive algorithms have fairly high complexity in the MIMO case, due to the large number (M N) of parallel filters required (where M is the number of transmit antennas and N the number of receive antennas in the MIMO system). The convergence time of the LMS-G algorithm for the channels of interest is 3 msec (for a 4×4 equalizer on the TU (Typical Urban) channel) which restricts its use to slowly moving mobile terminals.
Application of LMS algorithm in the frequency domain for a SISO TDMA (time division multiple access) system has also been proposed. This so-called FLMS (frequency LMS) algorithm operates in a block mode, using either overlap-add or overlap-save to perform the time domain linear convolutions. FLMS can be both less complex than ordinary LMS and offer faster convergence when an individual step-size is chosen for each frequency bin. The so-called TLMS (transform domain LMS) algorithms operate in a sample-by-sample mode and have substantially greater complexity than FLMS.